Week 5 BUS 308 assignment

Week 5 Correlation and Regression

For each question involving a statistical test below, list the null and alternate hypothesis statements.  Use .05 for your significance level in making your decisions.

For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.

1

Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.)

a. Interpret the results.  What variables seem to be important in seeing if we pay males and females equally for equal work?

2

Below is a regression analysis for salary being predicted/explained by the other variables in our sample  (Mid,

 age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways of

 expressing an employee’s salary, we do not want to have both used in the same regression.)

Ho: The regression equation is not significant.

Ha: The regression equation is significant.

Ho: The regression coefficient for each variable is not significant

Ha: The regression coefficient for each variable is significant

Sal

The analysis used Sal as the y (dependent variable) and

SUMMARY OUTPUT

mid, age, ees, sr, g, raise, and deg as the dependent 

variables (entered as a range).

Regression Statistics

Multiple R

0.99215498

R Square

0.9843715

Adjusted R Square

0.98176675

Standard Error

2.59277631

Observations

50

ANOVA

df

SS

MS

F

Significance F

Regression

7

17783.7

2540.52

377.914

8.44043E-36

Residual

42

282.345

6.72249

Total

49

18066

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-4.009

3.775

-1.062

0.294

-11.627

3.609

-11.627

3.609

Mid

1.220

0.030

40.674

0.000

1.159

1.280

1.159

1.280

Age

0.029

0.067

0.439

0.663

-0.105

0.164

-0.105

0.164

EES

-0.096

0.047

-2.020

0.050

-0.191

0.000

-0.191

0.000

SR

-0.074

0.084

-0.876

0.386

-0.244

0.096

-0.244

0.096

G

2.552

0.847

3.012

0.004

0.842

4.261

0.842

4.261

Raise

0.834

0.643

1.299

0.201

-0.462

2.131

-0.462

2.131

Deg

1.002

0.744

1.347

0.185

-0.500

2.504

-0.500

2.504

Interpretation:

 Do you reject or not reject the regression null hypothesis?

Do you reject or not reject the null hypothesis for each variable?

What is the regression equation, using only significant variables if any exist?

What does result tell us about equal pay for equal work for males and females?

3

Perform a regression analysis using compa as the dependent variable and the same independent

variables as used in question 2.  Show the result, and interpret your findings by answering the same questions.

Note: be sure to include the appropriate hypothesis statements.

4

Based on all of your results to date, is gender a factor in the pay practices of this company?  Why or why not?

Which is the best variable to use in analyzing pay practices - salary or compa?  Why?

5

Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?

What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?

Score:

Week 5

Correlation and Regression

<1 point>

1.    

Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)

a.

Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?

b. Place table here (C8):

c.

Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are

significantly related to Salary?

To compa?

d.

Looking at the above correlations - both significant or not - are there any surprises -by that I

mean any relationships you expected to be meaningful and are not and vice-versa?

e.

Does this help us answer our equal pay for equal work question?

<1 point>

2

Below is a regression analysis for salary being predicted/explained by the other variables in our sample  (Midpoint,

 age, performance rating, service,  gender, and degree variables. (Note: since salary and compa are different ways of

 expressing an employee’s salary, we do not want to have both used in the same regression.)

Plase interpret the findings.

Ho: The regression equation is not significant.

Ha: The regression equation is significant.

Ho: The regression coefficient for each variable is not significant

  Note: technically we have one for each input variable.

Ha: The regression coefficient for each variable is significant

  Listing it this way to save space.

Sal

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.9915591

R Square

0.9831894

Adjusted R Square

0.9808437

Standard Error

2.6575926

Observations

50

ANOVA

df

SS

MS

F

Significance F

Regression

6

17762.3

2960.38

419.1516

1.812E-36

Residual

43

303.7003

7.0628

Total

49

18066

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-1.749621

3.618368

-0.4835

0.631166

-9.046755

5.5475126

-9.04675504

5.54751262

Midpoint

1.2167011

0.031902

38.1383

8.66E-35

1.1523638

1.2810383

1.152363828

1.28103827

Age

-0.004628

0.065197

-0.071

0.943739

-0.136111

0.1268547

-0.13611072

0.1268547

Performace Rating

-0.056596

0.034495

-1.6407

0.108153

-0.126162

0.0129695

-0.12616237

0.01296949

Service

-0.0425

0.084337

-0.5039

0.616879

-0.212582

0.1275814

-0.21258209

0.12758138

Gender

2.4203372

0.860844

2.81159

0.007397

0.6842792

4.1563952

0.684279192

4.15639523

Degree

0.2755334

0.799802

0.3445

0.732148

-1.337422

1.8884885

-1.33742165

1.88848848

Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.

Interpretation:

For the Regression as a whole:

What is the value of the F statistic:

What is the p-value associated with this value:

Is the p-value <0.05?

Do you reject or not reject the null hypothesis:

What does this decision mean for our equal pay question:

For each of the coefficients:

Intercept

Midpoint

Age

Perf. Rat.

Service

Gender

Degree

What is the coefficient's p-value for each of the variables:

Is the p-value < 0.05?

Do you reject or not reject each null hypothesis:

What are the coefficients for the significant variables?

Using only the significant variables, what is the equation?

Salary =

Is gender a significant factor in salary:

If so, who gets paid more with all other things being equal?

How do we know?

<1 point>

3

Perform a regression analysis using compa as the dependent variable and the same independent

variables as used in question 2.  Show the result, and interpret your findings by answering the same questions.

Note: be sure to include the appropriate hypothesis statements.

Regression hypotheses

Ho:

Ha:

Coefficient hyhpotheses (one to stand for all the separate variables)

Ho:

Ha:

Place D94 in output box.

Interpretation:

For the Regression as a whole:

What is the value of the F statistic:

What is the p-value associated with this value:

Is the p-value < 0.05?

Do you reject or not reject the null hypothesis:

What does this decision mean for our equal pay question:

For each of the coefficients:

Intercept

Midpoint

Age

Perf. Rat.

Service

Gender

Degree

What is the coefficient's p-value for each of the variables:

Is the p-value < 0.05?

Do you reject or not reject each null hypothesis:

What are the coefficients for the significant variables?

Using only the significant variables, what is the equation?

Compa =

Is gender a significant factor in compa:

If so, who gets paid more with all other things being equal?

How do we know?

<1 point>

4

Based on all of your results to date,

Do we have an answer to the question of are males and females paid equally for equal work?

If so, which gender gets paid more?

 How do we know?

Which is the best variable to use in analyzing pay practices - salary or compa?  Why?

What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?

<2 points>

5

Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?

What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?